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son4ous [18]
3 years ago
11

A superhero is trying to leap over a tall building. The function f(x)=-16x^2+200x gives the superhero's height in feet as a func

tion of time. The building is 612 feet high. Will the superhero make it over the building
Mathematics
1 answer:
Gemiola [76]3 years ago
7 0

Answer:

Since \bigtriangleup \geq 0, the superhero makes it over the building.

Step-by-step explanation:

The height is given by the following function:

f(x) = -16x^{2} + 200x

Will the superhero make it over the building?

We have to find if there is values of x for which f(x) = 612.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

If \bigtriangleup < 0, the polynomial has no solutions.

In this question:

f(x) = -16x^{2} + 200x

-16x^{2} + 200x = 612

16x^{2} - 200x + 612 = 0

We have to find \bigtriangleup

We have that a = 16, b = -200, c = 612. So

\bigtriangleup = (-200)^{2} - 4*16*612 = 832

Since \bigtriangleup \geq 0, the superhero makes it over the building.

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atroni [7]

Answer:

D. P(5+ 6's) = 0.4063

Step-by-step explanation:

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For the distribution to be applicable, the experiment must

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3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.

4. Independence between trials.

Let  

n = number of trials  = 25

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x = number of successes  (0 ≤ x ≤ n)  = 5

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Applying binomial distribution

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For n = 25 trials with probability of success (roll a 6) = 1/6

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It is easier to calculate the complement by

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= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )

1- (

    P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961

    P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051

     P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532

    P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883

    P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171

)

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Answer:

$12.78.

Step-by-step explanation:

The discount is 20% so:

Total payment  before tax = 15 - (15 *20/100) = $12.

Now we add the 6.5% tax:

Total payment after tax = 12 + (12 * 6.5/`100) =  $12.78.

6 0
2 years ago
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Answer:
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